Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm?

acute, because 62 + 102 < 122
acute, because 6 + 10 > 12
obtuse, because 62 + 102 < 122
obtuse, because 6 + 10 > 12

Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

Answer:

it's the 3rd one

Answer: 4/35

Step-by-step explanation:

Number of red marbles = 4

Number of blue marbles = 5

Number of green marbles = 6

Total number of marbles = 4+5+6 = 15

When a red marble is picked, the probability is 4/15, then to pick a green marble after that, we have 14 marbles left and probability of picking green is 6/14.

Now, probability of choosing a red marble from the bag, not putting it back, and then choosing a green marble will be:

= 4/15 × 6/14

= 24/210

= 4/35

Answer:

The mean is 77.

Answer:

The mean of this equation is 77

Step-by-step explanation:

74+75+80+76+75+81+78​-539

Number of terms=7

539/7=77

Answer:

A. - This is my guess.

===================================================

Work Shown:

A = probability of landing on an odd number

A = 5/9 because there are 5 odd numbers out of 9 total

B = probability of getting heads

B = 1/2

C = landing on 3 on the spinner

C = 1/9

Multiply the values of A,B,C

A*B*C = (5/9)*(1/2)*(1/9) = (5*1*1)/(9*2*9) = 5/162

Note: The fraction 5/162 converts to the approximate decimal 0.03086 which then converts to 3.086%, when rounding to the nearest tenth of a percent we get 3.1%

The estimated total time for all five pools is approximately 13.85 hours.

To estimate the time required to install the fifth pool using the learning curve, we can use the formula:

Time for nth unit = Time for first unit * (n^b)

Where:

Time for nth unit is the estimated time to install the nth pool

Time for first unit is the estimated time to build the first pool (30 hours)

n is the number of units (in this case, n = 5 for the fifth pool)

b is the learning curve exponent (85% learning rate corresponds to b = log(0.85) / log(2))

Let's calculate the estimated time for the fifth pool:

b = log(0.85) / log(2) ≈ -0.157

Time for fifth pool = Time for first pool * (5^b)

Time for fifth pool = 30 * (5^(-0.157))

Calculating this, we find:

Time for fifth pool ≈ 30 * 0.6764 ≈ 20.29 hours

Therefore, the estimated time required to install the fifth pool is approximately 20.29 hours.

To calculate the total time for all five pools, we need to sum the time required for each pool from the first to the fifth. Since the learning curve assumes decreasing time with increasing units, we can use a summation formula:

Total time for all units = Time for first unit * ((1 - (n^b)) / (1 - b))

Using this formula, let's calculate the total time for all five pools:

Total time for all five pools = Time for first pool * ((1 - (5^b)) / (1 - b))

Total time for all five pools = 30 * ((1 - (5^(-0.157))) / (1 - (-0.157)))

Calculating this, we find:

Total time for all five pools ≈ 30 * 0.4615 ≈ 13.85 hours

Therefore, the estimated total time for all five pools is approximately 13.85 hours.

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The probability that two or less people will prefer travelling with brilliant taxis is 0.678

bt represnts brilliant taxis

tr represent taxi ride

P(bt) = 1/5

P(tr) = 4/5

Total number of people surveyed is n = 10

a) what is the probability that two or less people will prefer travelling with brilliant taxis

P(x<=2) = P(×=0) + P(×=1) + P(×=2)

Using Binomial probability

P(x<=x) = nCx(p)^x(q)^n-x

nCx = n!/(n-×)!(x!)

P(x<=2) = 10C0 (1/5)^0(4/5)^10 + 10C1 (1/5)^1(4/5)^9 + 10C2 (1/5)^2(4/5)^8

P(x<=2) = 1(1)(0.1074) +  10(0.2)(0.1342) + 45(0.04)(0.1677)

P(x<=2) = 0.1074 +  0.2684 + 0.3020

P(x<=2) = 0.6778

P(x<=2) = 0.678 ( 3d.p)

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The 85% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list is estimated to be between the lower endpoint and upper endpoint. The lower endpoint and upper endpoint need to be calculated using the given sample data.

To construct the confidence interval, we use the formula for the confidence interval for a proportion:

CI = p^ +- Z * sqrt((p^ * (1 - p^)) / n)

Where:

CI = Confidence Interval

p^ = Sample proportion (proportion of captured individuals in the sample)

Z = Z-score corresponding to the desired confidence level (85% confidence level corresponds to a Z-score of approximately 1.440)

n = Sample size (number of suspected criminals in the sample)

Given data:

Sample size (n) = 455

Number captured (x) = 109

First, calculate the sample proportion (p^):

p^ = x / n

Substituting the values:

p^ = 109 / 455 ≈ 0.239

Next, calculate the standard error:

SE = sqrt((p^ * (1 - p^)) / n)

Substituting the values:

SE = sqrt((0.239 * (1 - 0.239)) / 455) ≈ 0.020

Finally, calculate the lower and upper endpoints of the confidence interval:

Lower endpoint = p^ - Z * SE

Upper endpoint = p^ + Z * SE

Substituting the values:

Lower endpoint = 0.239 - 1.440 * 0.020

Upper endpoint = 0.239 + 1.440 * 0.020

Calculating:

Lower endpoint ≈ 0.209

Upper endpoint ≈ 0.269

Therefore, the 85% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list is approximately 0.209 to 0.269.

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Answer:

3 yards or option D.

Step-by-step explanation:

We can use the formula for the volume of a rectangular prism, which is:

Volume = length x width x height

We are given that the volume of the shower is 7.5 cubic yards, and the area of the base is 2.5 square yards. We can use the area of the base to find the length and width of the shower, since the base is a rectangle.

Area of base = length x width

2.5 = length x width

We are not given the length or width, but we can solve for one of them in terms of the other:

length = 2.5/width

Now we can substitute this expression for length into the formula for volume:

Volume = length x width x height

7.5 = (2.5/width) x width x height

Simplifying, we can cancel out the width terms:

7.5 = 2.5 x height

Dividing both sides by 2.5, we get:

3 = height

Answer:

fifth option is the correct ans

sin(thita) = -sqare root 2 / 2

The statements which are true are,

The measure of reference angle is 45° and tan (θ) = -1.

Reference number associated with t is defined as the shortest distance from the x axis to the terminal point t, along a unit circle.

Reference angle is shortest angle measure from the X axis to the terminal side of the angle.

Reference angle = 2π - 7π/4 = π/4 = 45°

We have,

7π/4 = 2π - π/4

We also know that,

cos(2π - x) = cos x,

sin (2π - x) = -sin x

tan (2π - x) = -tan x

So, using theses identities,

cos (7π/4) = cos (2π - π/4) = cos(π/4) = 1/√2

sin (7π/4) = sin (2π - π/4) = -sin (π/4) = -1/√2

tan (7π/4) = tan (2π - π/4) = -tan (π/4) = -1

Hence the true statements are The measure of reference angle is 45° and tan (θ) = -1.

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Answer: 24,179 - 3000y

Step-by-step explanation: Each year the car goes down by 3000 since you said it was decreasing, so y represents the year and you eould out it next to the 3000 to represent that 3000 is being decreased every year.

Step-by-step explanation:

Original cost = 900

Cost after VAT = 990

VAT amount = 990 - 900 = 90

Rate of VAT = 90/900×100 = 90/9 = 10%

The decision to use a univariable or multivariable regression model depends on the research question, data availability, model complexity, and goodness of fit.

What is the linear regression equation?

The formula for simple linear regression is Y = mX + b, where Y is the response (dependent) variable, X is the predictor (independent) variable, m is the estimated slope, and b is the estimated intercept.

When deciding whether to use a univariable or multivariable linear regression model, there are several factors to consider:

Research question: Consider the research question you are trying to answer. If you are interested in understanding the relationship between a single independent variable and a dependent variable, then a univariable regression model may be sufficient. However, if you want to explore the effect of multiple independent variables on a dependent variable, then a multivariable regression model may be more appropriate.

Data availability: Look at the data you have available. If you have only one independent variable that you believe is relevant to your research question, then a univariable regression model may be appropriate. However, if you have multiple independent variables that could potentially influence the dependent variable, then a multivariable regression model may be necessary.

Model complexity: Consider the complexity of the model you want to build. If you are interested in a simple linear relationship between an independent variable and a dependent variable, then a univariable regression model may be sufficient. However, if you believe that there are interactions between multiple independent variables that could affect the dependent variable, then a multivariable regression model may be necessary.

Model fit: Evaluate the goodness of fit of both univariable and multivariable models. Compare the R-squared values of each model to determine which model provides a better fit to the data. A higher R-squared value indicates a better fit between the independent and dependent variables.

Hence, the decision to use a univariable or multivariable regression model depends on the research question, data availability, model complexity, and goodness of fit.

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The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

From the question, we have the following parameters that can be used in our computation:

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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Step-by-step explanation:

the surface areas are always the sum of the areas of the individual sides and base area.

so, all we need to do here is calculating the areas of triangles, rectangles (actually squares) and a hexagon.

the area of a triangle is

baseline × height / 2

or with Heron's formula when we have all sides

s = (a+b+c)/2

area = sqrt(s×(s-a)×(s-b)×(s-c))

the area of a rectangle is

length × width

for a square that is then

side × side = side²

and the area of a regular hexagon can be created again as sum of multiple sub-shapes. but ultimately it is

3 × sqrt(3) × side² / 2

1.

square base area : 10×10 = 100 cm²

lateral areas :

one triangle is 10×13/2 = 65 cm²

4 triangles are then 4×65 = 260 cm²

total surface area :

100 + 260 = 360 cm²

2a.

3 lateral triangles :

3 × 8×10/2 = 120 units²

base area (Heron's, as all 3 sides are 8 units) :

s = 3×8/2 = 12

area = sqrt(12×4×4×4) = sqrt(3×4×4×4×4) = 16×sqrt(3)

total surface area :

120 + 16×sqrt(3) = 147.7128129... units²

2b.

4 lateral triangles :

4 × 8×10/2 = 160 units²

base area : 8×8 = 64 units²

total surface area :

160 + 64 = 224 units²

2c.

6 lateral triangles :

6 × 8×20/2 = 480 units²

base area :

3×sqrt(3)×8²/2 = 96×sqrt(3)

total surface area :

480 + 96×sqrt(3) = 646.2768775... units²

2d.

base area : 16² = 256 units²

4 lateral triangles. but we need to get their height first.

Pythagoras :

(16/2)² + 24² = height²

8² + 24² = height²

64 + 576 = height²

height² = 640

height = sqrt(640) = sqrt(64×10) = 8×sqrt(10)

4 triangles are

4 × 16×8×sqrt(10)/2 = 256×sqrt(10) units²

total surface area :

256 + 256×sqrt(10) = 256×(1 + sqrt(10) = 1,065.543081... units²

The explicit formula for geometric sequence calculator is  n = a 1 + r^(n-1) (n-1)

We can easily determine the value of any term in the sequence using the formula once you have those values.

where:

The sequence's nth word is a n.

The first term in the series is a 1.

The frequency of successive terms is expressed as r.

The sequence's length, n, is given.

The values of a 1, r, and n must be known in order to use this algorithm as a geometric sequence calculator. You can easily determine the value of any term in the sequence using the formula once you have those values.

Therefore, the explicit formula for geometric sequence calculator is  n = a 1 + r^(n-1) (n-1).

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Answer:

\(d=\frac{2w(c-2)}{5} \)

Step-by-step explanation:

The given formula is:

c=5d+4w/2w

We need to find d.

Multiply 2w on both sides, we get

c x 2w= 5d+4w/2w x 2w

2cw=5d+4w

Adding -4w on both sides, we get

2cw-4w=5d+4w-4w.

2cw-4w=5d

2w(c-2)=5d

Dividing by 5, we get

2w(c-2)/5 = 5d/5

2w(c-2)/5 = d

Hence the required formula with subject d is

\(d=\frac{2w(c-2)}{5} \)

Answer:

Its SAS( side angle side) axiom.

Step-by-step explanation:

Here are the steps required for Solving Quadratics by Factoring:

Step 1: Write the equation in the correct form. To be in the correct form, you must remove all parentheses from each side of the equation by distributing, combine all like terms, and finally set the equation equal to zero with the terms written in descending order.

Step 2: Use a factoring strategies to factor the problem.

Step 3: Use the Zero Product Property and set each factor containing a variable equal to zero.

Step 4: Solve each factor that was set equal to zero by getting the x on one side and the answer on the other side.

Example 1 – Solve: x2 + 16 = 10x

Step 1: Write the equation in the correct form. In this case, we need to set the equation equal to zero with the terms written in descending order.

Step 1

Step 2: Use a factoring strategies to factor the problem.

Step 2

Step 3: Use the Zero Product Property and set each factor containing a variable equal to zero.

Step 3

Step 4: Solve each factor that was set equal to zero by getting the

No, the sample in this case is not random.

The sample in this case is not random. Random sampling involves selecting individuals from a population in such a way that each individual has an equal chance of being selected. In the given scenario, the sample consists only of students who buy hot lunch on a particular day.

This sampling method is not random because it introduces a bias by including only a specific subgroup of students who have chosen to buy hot lunch. It does not provide an equal opportunity for all students in the population to be selected for the survey.

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The function f(x) = -4x² - 5x/x² - 2x + 1 is a rational function, and its domain is the set of all x for which the denominator is not equal to zero. In this case, the denominator is x² - 2x + 1.

To find the values of x for which the denominator is not equal to zero, we can solve the quadratic equation x² - 2x + 1 = 0. By factoring, we get (x - 1)² ≠ 0, which simplifies to (x - 1)(x - 1) ≠ 0, and further simplifies to (x - 1)² ≠ 0. This equation implies that x ≠ 1.

Therefore, the domain of f is given by Dom(f) = (-∞, 1)U(1, ∞), which means that the function is defined for all values of x except x = 1.

Since f is a ratio of two polynomials, it is continuous on its domain, which is the interval (-∞, 1)U(1, ∞).

Hence, the interval(s) over which the function f(x) = -4x² - 5x/x² - 2x + 1 is continuous are (-∞, 1)U(1, ∞).

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Answer:

Lake A

Step-by-step explanation:

FIrst off I am not sure how this connects with the lake but based on what I have seen and learned so far I would say that the Answer to #3 on the last question is Lake A and for the second part based on the data set I am unsure of how to do that but at least u got the answer to #3? sorry if this is no help.

Answer:

Total is 24

HALF THE TOTAL- 12

Impossible event- Picking a black marble

Certainty- Picking either one of a green, red, or blue marble

As likely as not event would be picking a blue marble(probability of that is 12/24= 1/2)

More likely than not event would be picking either a red or blue marble whose probability in total is 18/24= 3/4.

Unlikely event- You not picking anything at all

Step-by-step explanation:

Hi. Took me some time to attempt all problems, but the key to solving these problems is to ahve a firm foundation of basic probability. Things like likeliness and unlikelieness are all outskirts of probability, so I would reccomend getting yourself familiar with those basics. You GOT THIS!

In the event  of alteration in the rate at which the water level of the funnel is changing when the water is 15 inches high is 0.42 cubic inches per second.
The volume of a cone is given by the formula V = (1/3)πr²h here r is the radius of the base and h is the height of the cone.

Now we have differentiate this formula concerning t to get
dV/dt = (1/3)πr²dh/dt + (2/3)πrh²dr/dt.

It is given to us  that water is coming out a giant cone shaped funnel at a rate of 15 cubic inches per second, then we  can say that
dV/dt = -15 cubic inches per second

Therefore the funnel has a maximum radius of 40 inches and a height of 75 inches. We need to evaluate  dh/dt
If h = 15 inches.

In order to find dh/dt,
we need to evaluate  dr/dt and place it in  equation for dV/dt.

Therefore, to find dr/dh = r/h.
Given
when h = 75 inches,
r = 40 inches.
Therefore, dr/dh
= 40/75.

Staging this into the equation for dV/dt,

-15 = (1/3)π(40²)(dh/dt) + (2/3)π(40)(15)²(40/75)

Here simplification takes place


dh/dt = -0.4π/3
≈ -0.42 cubic inches per second
In the event  of alteration in the rate at which the water level of the funnel is changing when the water is 15 inches high is 0.42 cubic inches per second.


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Answer:

∠ E ≈ 38.9° , ∠ G ≈ 79.6°

Step-by-step explanation:

given 3 sides of a triangle, to find any of the angles use the Cosine rule

(A)

cos E = \(\frac{f^2+g^2-e^2}{2fg}\)

where f is the fide opposite ∠ F , g is the side opposite ∠ G and

e is the side opposite ∠ E

here f = EG = 42 , g = EF = 47 and e = FG = 30 , then

cos E = \(\frac{42^2+47^2-30^2}{2(42)(47)}\) = \(\frac{1764+2209-900}{3948}\) = \(\frac{3073}{3948}\) , then

∠ E = \(cos^{-1}\) ( \(\frac{3073}{3948}\) ) ≈ 38.9° ( to the nearest tenth )

(b)

similarly, using e, f , g as above in part A

cos G = \(\frac{e^2+f^2-g^2}{2ef}\) = \(\frac{30^2+42^2-47^2}{2(30)(42)}\) = \(\frac{900+1764-2209}{2520}\) = \(\frac{455}{2520}\) , then

∠ G = \(cos^{-1}\) ( \(\frac{455}{2520}\) ) ≈ 79.6° ( to the nearest tenth )

The lowest term of the given expression after simplifying the fractions are 3(x - 2/3)(x - 3)/(x - 5)(x + 3) - 2x(x - 1)/(2x + 1)

1. To reduce the expression x^2 - 9x/28x + 15 to lowest terms, we first factor the numerator and denominator:

x^2 - 9x + 15 = (x - 3)(x - 5)
28x + 15 = 7(4x + 3)

So the expression becomes (x - 3)(x - 5)/7(4x + 3). We cannot simplify this any further, so the answer is (a) x - 3/x + 5.

2. To simplify a^2 - 25/a^2 - 3a - 15, we first factor the numerator and denominator:

a^2 - 25 = (a + 5)(a - 5)
a^2 - 3a - 15 = (a - 5)(a + 3)

So the expression becomes (a + 5)(a - 5)/(a - 5)(a + 3). We can cancel out the (a - 5) term, so the answer is (c) a(a - 5)/3.

3. To simplify 3x^2 - 4x + 6/x^2 - 2x - 15 - 2x^2/2x + 1, we first combine the numerator of the first fraction:

3x^2 - 4x + 6 = 3(x^2 - (4/3)x + 2)

Then we factor the denominator of the first fraction:

x^2 - 2x - 15 = (x - 5)(x + 3)

We can also factor the numerator of the second fraction:

-2x^2 = -2x(x - 1)

And finally, we factor the denominator of the second fraction:

2x + 1 = (2x + 1)

Putting it all together, we have:

3(x - 2/3)(x - 3)/(x - 5)(x + 3) - 2x(x - 1)/(2x + 1)

We cannot simplify this any further, so this is the answer.

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Answer: -108y^2 + 84y

Step-by-step explanation:

y^2 is y squared

give me brainiest! :D

The required simplified solution of the given expression is -108y² + 84y.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,

Given expression,
= −12y(9y − 7).

Simplify,
Applying distributive property,
= -12y×9y - 12y(-7)
= -108y² + 84y

Thus, the required simplified solution of the given expression is -108y² + 84y.

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